New Hepwm Optimization In Three Ohase Inverter

“I hereby declare that I have read through this report entitle “New Optimization method in Three-Phase inverter” and found that it has comply the partial fulfillment for awarding the degree of Bachelor of Electrical Engineering (Power Electronics and Drive)”

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NEW HEPWM OPTIMIZATION METHOD IN THREE PHASE INVERTER

NOR AZIZAH BINTI MOHD YUSOFF

A report submitted in partial fulfillment of the requirements for the Bachelor Of Electrical Engineering (Power Electronics and Drive)

Faculty of Electrical Engineering

UNIVERSITI TEKNIKAL MALAYSIA MELAKA

I declare that this report entitle “New HEPWM Optimization method in Three-Phase Inverter” is the result of my own research except as cited in the references. The report has not been accepted for any degree and is not concurrently submitted in candidature of any other degree.

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ACKNOWLEDGEMENT

First and foremost, many thanks to Allah SWT for blessing me with good health and lots of patience in completing this project. My greatest appreciations and thank you to my supervisor, Puan Hazilina Binti Bahari for guiding, supervising and also advising me to complete this final year project successfully.

My deepest gratitude goes to two most important people who always given their loves and support, Mak and Abah; thank you will never seems enough to depict my appreciation. For the generous assistance in implementing various experiments, I would like to acknowledge my course mates. Thanks for all the times spent and the never ending patience. I really owe this to you guys.

ABSTRACT

ABSTRAK

TABLE OF CONTENT

CHAPTER TITLE PAGE

AKNOWLEDGMENT v

ABSTRACT vi

TABLE OF CONTENT viii

LIST OF FIGURE x

1 INTRODUCTION

1.1 Background 1

1.2 Project overview 1

1.3 Problem Statement

1.1.1 High Harmonic Distortion at low Frequency. 2 1.1.2 Determine the suitable switching angle 2 1.3 Project Objectives

1.4 Project Scope 3

1.5 Method of Analysis 4 1.6 Project Report Summary 5

1 THEORY AND LITERATURE REVIEW

2.1 Introduction 6

2.2 Fundamental switching Angle 6 2.3 Harmonics Elimination Pulse Width Modulation 7

(HEPWM)

2.5 Differential Evolution Theorem 12

2.5.1 Population Structure 12

2.5.2 Initialization 13

2.5.3 Mutation 14

2.5.4 Crossover 14

2.6 Applying Differential Evolution Theorem in 16

HEPWM to Determine Switching Angle. 2.7 Voltage Source Inverter 17

2.8 The Six-step Inverter 17

2.9 Total Harmonic Distortion 19

3 METHODOLOGY 3.1 Introduction 21

3.2 Concept Of Project 21

3.3 Differential Evolution Implementation 22

3.3.1 Initialization 23

3.3.2 Mutation 23

3.3.3 Recombination 24

3.3.4 Selection 24

3.5 Voltage Source Inverter 27

3.6 Total Harmonic Distortion (THD) 28

3.7 MATLAB version 6.5 29

4 RESULT AND DISCUSSION 4.1 Introduction 30

4.2 Result (Differentian Evolution Algorithm) 30

4.3 Manual Calculation Output 31

4.4 HEPWM Waveform Design 33

4.5 Simulation result using MATLAB 35

4.8 Circuit Voltage Source Inverter (MATLAB) 38 4.9 Simulation Result

4.9.1 Voltage Source Inverter (Line to Line) 39 4.9.2 Voltage Source Inverter (Line to Line) 40 4.10 Analysis and Discussion 41 4.11 Fast-Fourier Transformed Analysis (FFT) 41

5 CONCLUSION

5.1 Introduction 43

LIST OF FIGURES

TABLE TITLE PAGE

2.2 PWM output waveform with selective switching angle 7

2.4 Generalized quarter-wave symmetric PWM waveform 8

2.6 Flow of DE’s generate-and-test loop 17

2.8 (a) Three phase inverter circuit. 18

2.8 (b) Switching sequence, line-to-neutral voltage and line 19

Current output waveform 3.1 The overview of project 22

3.2 Flow the basic in Differential Evolution algorithm 23

3.4 Flow chart DE for HEPWM 26

3.5 Three Phase Voltage Source Inverters 27

3.6 Step to observed THD 28

4.1 (a) – (d) Trajectories of solution for programmed PWM 31

4.2 HEPWM waveform design 33

LIST OF TABLES

TABLE TITLE PAGE

4.1 Data for m = 3 and NP = 0.45 32

4.2 Data for m = 5 and NP = 0.45 32

4.3 Data for m = 7 and NP = 0.45 32

4.4 Data for m = 9 and NP = 0.45 33

4.5 HEPWM waveform design 34

4.7 Inverter Parameter 35

CHAPTER 1

INTRODUCTION

This chapter will described about the introduction of this project which includes the overview of the whole project, the problem statement that occur before this entire project will be complete. The objectives and scope that are needed as a fulfillment of this project are completely described in this chapter.

1.1 Project Overview

their controlled turn-on and turn off. In this project the concept of HEPWM technique is described with performance analysis of waveform. Total Harmonic Distortion (THD) is helped to proof the calculation by showing the reduction value of THD. Finally, the simulation result with all analysis for the strategy applies in differential evolution and for three phase inverter using HEPWM is presented.

1.2 Problem Statement

1.1.1 High Harmonics distortion at low frequency.

1.1.2 Determine the suitable switching angle.

Differential Evolution will be used to determine the value switching angle for PWM to reduce distortion by eliminating the harmonic until higher harmonic order by produces the amplitude voltage at a fundamental frequency to be zero.

1.3 Project Objectives

The objectives of this project are:

i. To determine the suitable switching angle until to eliminate harmonic order by using Differential Evolution algorithm using M-file of MATLAB 6.5.

ii. To simplify the programming of differential evolution by using looping method in MATLAB 6.5.

iii. To design the circuit for HEPWM and VSI circuit and obtain the computer simulation results using Simulink-MATLAB 6.5.

1.4 Project Scope

The scope of work need to be done in this project will be more to analysis the concept of Differential Evolution method programmed using Simulink-MATLAB 6.5. This technique will be used to obtain the quality output waveform of HEPWM with lower harmonics before applied to VSIs by finding the accurate value switching angle under higher harmonic order condition. Since the computer simulation involving MATLAB software, my supervisor had narrowed the using two kinds of method that contain in it which is M-File and Simulink-Block diagram. But, using Simulink-MATLAB 6.5, both HEPWM and VSIs output waveform from the simulation result will be presented and analyzed.

other strategy that are needed in this simulation has been done.

1.5 Method of Analysis

This project performed in two stages. The first stage deals with the programmed process to get proved the expected result of HEPWM technique and VSIs process. This involves the using of M-File MATLAB 6.5 to simulate the method of differential evolution in order to find the number of switching angle which will obtain all the result in term of the best number of switching angle and also the trajectories curve after complete the iteration or commutation according to the equation of Fourier Series that apply in Differential Evolution Method. Then, the result for this method will be analyzed and compared the strategy of differential method based once their complete the commutation.

1.6 Project Report Summary

This project report contains of five chapters which will describe this project details. The first chapter is the introduction part where in this chapter, the overall description of the project is highlighted. The objectives of this project, the scopes and the methodology are described.

Second chapter of this report will be discussing about the research and analysis of this project. Each of the facts and the information from the analysis will be explained.

The third chapter will describe the method used in implement the project task. The technique and methodology of this project is split into two major part that is programmed M-File and Simulink-Block diagram. In this chapter, each part will be described in depth.

The fourth chapter will described is the most important part that is the result for this project. In this chapter all of result will be showed include the entire figure for each harmonic number and the analysis and discussion about entire of result include the equation of formula that being used. All of analysis and discussion that had been done will be stated clearly. The analysis is using the two kind’s method in MATLAB 6.5.

CHAPTER 2

THEORY AND LITERATURE REVIEW

This chapter will described about the background of this project and the literature review which includes the previous related project and the development made by the people in Electronic Engineering Field all over the world and the mathematicians people that developed the equation in differential evolution method.

2.1Introduction

2.2Fundamental of Switching Angle.

According to book Power Electronics Handbook-Device, Circuit and Application, 2nd Edition by Muhammad H. Rasyid , switching angle or conducting angle can be chosen to reduce the total of harmonics distortion. Normally, we choose the minimum angle of PWM wave so that the major lower frequency harmonics can be eliminated.

Figure 2.2: PWM output waveform with selective switching angle

2.3Harmonics Elimination Pulse Width Modulation (HEPWM)

pre-calculated switching angles into an EPROM or microprocessor memory. This allows Online generation of switching angle by using look-up tables or BCD down-counter to generate pulse width in time domain.

2.4Generalized Method of Harmonic Elimination Pulse-Width Modulation (HEPWM)

A generalized quarter-wave symmetric PWM pole switching can be defined as shown in Figure 2.4. Through this figure, there is a half cycle with M chops and in negative cycle is a symmetric for this M chop [1] The basic square wave is chopped a number of times and a fixed relationship between the number of chops and possible number of harmonics that can be eliminated is derived. The periodic waveform can be noted as half-wave symmetry and unit amplitude [1] Therefore:

( ) = − ( − ) (1)

( ) = M chop per half cycle of two state periodic functions. Let , … . define the M-chops as shown in Figure 2.1 below.

The Fourier series equation can be use to determine the waveform, below is the equation of Fourier series:

( ) = ∞ [ sin(nωt) + cos(nωt)] (2)

Where

= ∫ ( ) sin( ) ( ) (3)

= ∫ ( ) cos( ) ( ) (4)

By substituting f (( ) in equation (3) included the property of half-wave symmetry:

= 2 (1) sin( ) ( ) (5)

Where = 0, = , and < < … . < Evaluating the integral for (4),

= ∑ (−1) [cos( )−cos ( ] (6)

= 2 cos −cos + 2 (−1) cos

But and = . Hence,

cos = 1

cos = (−1)

Similarly

=− ∑ (−1) sin (8)

For even number the property of half-wave symmetry can be determined the waveform for = 0 and = 0 as followed equation:

= [1 + 2∑ (−1) cos ] (9)

= [− ∑ (−1) sin ] (10)

Equation (9) and (10) are function of 2 variable … . To find the unique of 2M variable, the 2M equation is needed. By equating any harmonic to zero, 2 equation is derived from equation (9) and (10).

The equation is derived by equating = 0 for values of and it solved by letting ( ) as quarter-wave symmetry.

( ) = ( − )

Regarding to Figure 2.1, below is the relation of common quarter-wave symmetry:

= − (11)

For = 1,2, … … Therefore,

= sin ( − )

= [sin cos −cos sin ] (12)

sin = 0,

sin = −1

Substituting (11)

sin = sin ,

For = 1,2, … (13) Substituting (12) in (9), we get

= 4 (sin −sin _{( )}) = 0

From (10):

cos = cos ( − ( )) (14)

For = 1,2, … . For odd , (13) becomes

cos =−cos ₎ (15)

For = 1,2, … . Substituting (14) into (8), we get

= [1 + 2∑ (−1) cos ] (16)

Referring to figure 2.4, the elimination of M harmonic can be determined by solving M equation by letting equation 15 to be zero. HEPWM are created by Patel and Hoft [6] design to reduce harmonic of PWM spectra.

equations are non-linear and transcendental in nature; restricting it to off-line approach. There is no general solution for these types of equations and the transcendental nature of the equations suggests a possibility of multiple solutions [6-7]. For off-line computation, various numerical techniques are possible; most common is the Newton-Raphson method as done by the Patel and Hoft.. However, if the initial value is not correctly chosen, it can result in large iteration cycles.

2.5Differential Evolution Theorem

Evolutionary algorithm is new class of non-calculus, search and optimization technique that has become very popular in many engineering applications. These methods search from a population of points instead of a single point as in conventional search and optimization processes. Furthermore they do not require a “suitable” initial value. The initial points can be randomly generated from the search space. Genetic algorithm (GA) is one example of evolutionary algorithm that has been used associated with HEPWM [5]. Differential evolution (DE) algorithm is known to be a simple and fast evolutionary algorithm. It is similar to GA but with one main difference: DE adopts a mutation strategy that allows it to be self adaptive in the selection process [6]. Compared to GA, it consumes much shorter time to reach optimum point [6], [7]. Although recently introduced (in relation to other evolutionary algorithms), DE has been widely used in optimization problem. In this work, only DE is used to search for the HEPWM angles that will eliminate specified number of harmonics without comparing to latest advanced algorithms.